You're sure this is what Moynier and Fiddler call the "NE" couloir? Because M & F rate it class 4-5 snow and ice, but I was up there in late August and, apart from getting past the bergschrund, it was low-angle snow, in accordance with what both Croft and Secor had led be to believe. Looking at the M & F guidebook, their photo does show the line going up the N. couloir (and it agrees with their verbal description), but perhaps they're mistaken. I haven't been on the left, NE couloir, but it sounds icy, and it would make sense if M & F really meant this one and simply made an error.

Have you been on both the N and NE couloirs? Does the N. couloir really get icy? It simply doesn't seem steep enough.

The first time I climbed the couloir it had avalanched, scouring the snow down to ice, so it was a pure alpine/water ice climb from the bergschrund to the fork in the couloir. Much harder to climb than when I last did it as a snow climb!

I am 100% sure. Look at the picture in M&F High Sierra and they show the route up NE Couloir via the wide couloir right off the buttress that splits N and NE couloirs. This wide couloir (that I call North) DOES get ice, we encountered solid ice when descending it in mid-October 2005. When I went up this route in late July 2006, it was all snow and except for shrund it was quite easy. I agree that the 4-5 rating in M&F is overated, it is probably same or less steep than e.g. Dana Couloir.
I think Secor has this right, the wide one is North Couloir, the narrow one, which is steeper and was solid ice, is NE. Also, both M&F and Secor that first party descended this route (the wide North Couloir) on the first climb of the peak and there is no way (IMHO) that they would descend the narrow NE couloir, unless they were smoking something :-)Makes sense?

to take the left fork before heading right! Following the main couloir to the right leaves several pitches worth of climbing before reaching the summit block.

In later season the left fork melts out in sections, so look closely to see where to climb through rock bands to stay on course.

If you do end up climbing too far to the right, stay to the left (east) of the ridge crest until you reach the final notch before the Lightning Rod before cutting to the right (west) side. Cutting over too early is a bad idea.